Congruence is the state achieved by coming together, the state of agreement. The Latin congruō meaning “I meet together, I agree”. As an abstract term, congruence means similarity

Similarity (geometry)

Two geometrical objects are called similar if they both have the same shape. More precisely, either one is congruent to the result of a uniform scaling of the other...

 between objects. Congruence, as opposed to equivalence or approximation, is a relation which implies a kind of equivalence, though not complete equivalence.

Mathematics

• Congruence (geometry)
  Congruence (geometry)
  In geometry, two figures are congruent if they have the same shape and size. This means that either object can be repositioned so as to coincide precisely with the other object...
  
  , being isometric — roughly, the same size and shape
• In modular arithmetic
  Modular arithmetic
  In mathematics, modular arithmetic is a system of arithmetic for integers, where numbers "wrap around" after they reach a certain value—the modulus....
  
  , having the same remainder when divided by a specified integer
• Congruence or congruence relation
  Congruence relation
  In abstract algebra, a congruence relation is an equivalence relation on an algebraic structure that is compatible with the structure...
  
  , in abstract algebra, an equivalence relation on an algebraic structure that is compatible with the structure
• Congruence subgroup
  Congruence subgroup
  In mathematics, a congruence subgroup of a matrix group with integer entries is a subgroup defined by congruence conditions on the entries. A very simple example would be invertible 2x2 integer matrices of determinant 1, such that the off-diagonal entries are even.An importance class of congruence...
  
  , a subgroup defined by congruence conditions on the entries of a matrix group with integer entries
• Ramanujan's congruences
  Ramanujan's congruences
  In mathematics, Ramanujan's congruences are some remarkable congruences for the partition function p. The Indian mathematician Srinivasa Ramanujan discovered the following*p\equiv 0 \pmod 5*p\equiv 0 \pmod 7...
  
  , congruences for the partition function, p(n), first discovered by Ramanujan in 1919
• Congruence of squares
  Congruence of squares
  In number theory, a congruence of squares is a congruence commonly used in integer factorization algorithms.-Derivation:Given a positive integer n, Fermat's factorization method relies on finding numbers x, y satisfying the equality...
  
  , in number theory, a congruence commonly used in integer factorization algorithms
• Congruence (manifolds)
  Congruence (manifolds)
  In the theory of smooth manifolds, a congruence is the set of integral curves defined by a nonvanishing vector field defined on the manifold.Congruences are an important concept in general relativity, and are also important in parts of Riemannian geometry....
  
  , in the theory of smooth manifolds, the set of integral curves defined by a nonvanishing vector field defined on the manifold

• Congruence (general relativity)
  Congruence (general relativity)
  In general relativity, a congruence is the set of integral curves of a vector field in a four-dimensional Lorentzian manifold which is interpreted physically as a model of spacetime...
  
  , in general relativity, a congruence in a four-dimensional Lorentzian manifold that is interpreted physically as a model of space time, or a bundle of world lines
  • Zeller's congruence
    Zeller's congruence
    Zeller's congruence is an algorithm devised by Christian Zeller to calculate the day of the week for any Julian or Gregorian calendar date.- Formula :For the Gregorian calendar, Zeller's congruence is...
    
    , an algorithm to calculate the day of the week for any date

Psychology

• In Carl Rogers
  Carl Rogers
  Carl Ransom Rogers was an influential American psychologist and among the founders of the humanistic approach to psychology...
  
   personality theory, the compliance between ideal self and actual self. See Incongruence.
• In psychology and NLP (Neuro-linguistic programming
  Neuro-linguistic programming
  Neuro-linguistic programming is an approach to psychotherapy, self-help and organizational change. Founders Richard Bandler and John Grinder say that NLP is a model of interpersonal communication and a system of alternative therapy which seeks to educate people in self-awareness and effective...
  
  ), congruence could be defined as rapport within oneself, or internal and external consistency, perceived by others as sincerity or certainty.
• Mood congruence
  Mood congruence
  In psychiatry, mood congruence is the congruence between feeling, or the emotion that a person is experiencing, and affect display, or the manner in which that emotion is "presenting", or being expressed....
  
  ,

in psychiatry, congruence between feeling or emotion, and affect display or the manner in which that emotion is being expressed

in psychology, consistency between a patient's symptoms and their mood or mental disorder

Other

• Congruence bias
  Congruence bias
  Congruence bias is a type of cognitive bias similar to confirmation bias. Congruence bias occurs due to people's overreliance on direct testing of a given hypothesis, and a neglect of indirect testing.-Examples:...
  
  , a type of cognitive bias, similar to confirmation bias
• An alternative definition of congruence in the work of Virginia Satir
  Virginia Satir
  Virginia Satir was an American author and psychotherapist, known especially for her approach to family therapy and her work with Systemic Constellations...
  
  , one of the sources of NLP, is the balance between self, other and context.
• In cladistics, congruence is a test of homology
  Homology (biology)
  Homology forms the basis of organization for comparative biology. In 1843, Richard Owen defined homology as "the same organ in different animals under every variety of form and function". Organs as different as a bat's wing, a seal's flipper, a cat's paw and a human hand have a common underlying...
  
  , or shared, derived character states, in which the distributions of supposed homologies among taxa are compared for consistency.
• Horizontal and vertical congruence, two related principles of grouping
• In HTML
  HTML
  HyperText Markup Language is the predominant markup language for web pages. HTML elements are the basic building-blocks of webpages....
  
  , the graphical symbol for congruence ≅ is written as ⑃ (hexadecimal), ≅ (decimal) and ≅ (named entity).